Company profit

[gmatblood]

A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
0.5
1.0
1.5
2.0
4.0

OA: 2.0

[shankar.ashwin]

Let the company sell 100 units for $100 each. Total revenue = 10000
Now price drops by 50% ($50) but revenue remains unchanged .

X*50 = 10000
X = 200 - 100% increase.

You are asked %increase(units) / % decrease(cost) = 100/50 = 2

[neelgandham]

The question states that the total revenue remains unchanged after the discount. As, you know that the total revenue is a product of number of products and the price of the product, the total revenue is equal to price * number of units sold.

Let the initial price of the product be I, Then the discounted price of the product is 0.5*I
Let the number of the units sold before discount be U, and the number of units sold after discount be u

Total revenue = I*U = 0.5*I*u
Implies, u = 2U, i.e. a 100% increase in the number of units sold.

Ratio of the percent increase in the units sold to the percent decrease of the original price for this product = 100%/50% = 2.0

Answer D

[saketk]

let the number of initial units = 10
Initial cost = 10

Total amount = 10*10 = 100

Final cost = 5
So, the number of units must be 20 to make the product =100

i.e. 100% increase

Ration - [spoiler]100/50 = 2[/spoiler]